The Number We Have Known for 4,000 Years — But Still Do Not Fully Understand
√2 can be drawn with a square, approximated with astonishing accuracy, and proved irrational in a few lines. Yet its digits still hide questions mathematics cannot yet answer.
Nearly four thousand years ago, somewhere in ancient Mesopotamia, someone pressed a stylus into a small piece of wet clay.
The tablet shows a square, its diagonals, and several numbers written in the Babylonian base-60 system. Today it is known as YBC 7289, and it is one of the most remarkable surviving mathematical objects from the ancient world.
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Babylonian clay tablet YBC 7289, with modern annotations identifying the inscribed numbers. The diagonal records the sexagesimal approximation 1;24,51,10 for √2, equivalent to 1.41421296…, while the tablet also shows a square side of 30 and a corresponding diagonal of 42;25,35. Source: Urcia, A., Yale Peabody Museum of Natural History; labeled derivative by Theodor Langhorne Franklin. Wikimedia Commons, CC0 1.0.
Along one diagonal appears the number 1; 24, 51, 10. In our decimal notation, this means
Color me unimpressed. Those Babylonians clearly just measured the diagonal on that clay tablet with a Babylonian base-60 ruler. If they had been more precise they would have discovered 0 in the 108th position.
